CHAPTER 7: INTEGRALS
Class 12 CBSE Mathematics Core High-Efficiency Formula Sheet
1. Indefinite Integrals Blueprint
Integration is the inverse operation of differentiation.
Algebraic / Transcendental Function Primitive Evaluation Result ∫ f(x)dx
xn (xn+1) / (n+1) + C (n ≠ -1)
1/x ln|x| + C
sec2x tan x + C
1 / (x2 + a2) (1/a) tan-1(x/a) + C
1 / √(a2 - x2) sin-1(x/a) + C
2. Integration By Parts (ILATE Protocol)
∫ f(x)g(x) dx = f(x)∫g(x)dx - ∫[f'(x) · ∫g(x)dx] dx
Choose the first function f(x) based on priority order: Inverse, Logarithmic, Algebraic, Trigonometric,
Exponential.
3. Definite Integral King's Identity Property
∫ab f(x) dx = ∫ab f(a + b - x) dx
The Power of 'No': To be a topper, you have to say 'no' to the things that don't matter right now—extra sleep,
mindless scrolling, or hanging out. The result day will prove it was worth it. ego never accepts defeat.
Chapter 7 Notes • Page 1
Class 12 CBSE Mathematics Core High-Efficiency Formula Sheet
1. Indefinite Integrals Blueprint
Integration is the inverse operation of differentiation.
Algebraic / Transcendental Function Primitive Evaluation Result ∫ f(x)dx
xn (xn+1) / (n+1) + C (n ≠ -1)
1/x ln|x| + C
sec2x tan x + C
1 / (x2 + a2) (1/a) tan-1(x/a) + C
1 / √(a2 - x2) sin-1(x/a) + C
2. Integration By Parts (ILATE Protocol)
∫ f(x)g(x) dx = f(x)∫g(x)dx - ∫[f'(x) · ∫g(x)dx] dx
Choose the first function f(x) based on priority order: Inverse, Logarithmic, Algebraic, Trigonometric,
Exponential.
3. Definite Integral King's Identity Property
∫ab f(x) dx = ∫ab f(a + b - x) dx
The Power of 'No': To be a topper, you have to say 'no' to the things that don't matter right now—extra sleep,
mindless scrolling, or hanging out. The result day will prove it was worth it. ego never accepts defeat.
Chapter 7 Notes • Page 1
